摘要：Motivation. Quantile testing is a key technique for fitting parameters and testing performance in workers compensation experience rating and the number of quantile intervals must be specified for such a test. Method. A model is developed to compare the error in the quantile test empirical estimates of relative pure loss ratios to the interquantile differences between expected pure loss ratios. The ratio of these two quantities can be interpreted as a kind of noise-to-signal ratio which must be kept below a certain tolerance for the results of the quantile test to be sufficiently clear in a statistical sense. The formula for this ratio is a function of the random variation in individual risk loss ratios, a measure of the variation in experience modification (mod) values, the sample size of risks, and the number of quantiles. Theoretical model predictions are compared to empirical results from bootstrap quintile tests of the National Council on Compensation Insurance (NCCI) Experience Rating Plan (ERP). A generic type of individual risk credibility, though very different from the credibility values in the ERP, can be used to estimate the ratio of the standard deviation in individual risk loss ratios to a measure of variation in the mod values. Results. The model predicts that the noise-to-signal ratio grows in proportion to the 1.5 power of the number of quantiles and in inverse proportion to the 0.5 power of the sample size of risks. Empirical quintile and decile tests of NCCI’s Experience Rating Plan are consistent with model predictions. Conclusions. Increasing the number of quantiles requires a much greater proportional increase in data volume to maintain a constant noise-to-signal ratio. Combined with the typical large magnitude of individual-risk loss process variance to loss parameter variance, this explains the use of few quantiles, specifically quintiles, for testing NCCI’s Experience Rating Plan.
